This invention is in the technical field of coil design, for example, for use in nuclear magnetic resonance (NMR) applications.
This invention relates to means for providing a magnetic field with a uniform gradient suitable for use in NMR applications. A classic approach to this purpose has been to use a pair of loop coils known as the Maxwell pair, characterized as being placed symmetrically about the sample, carrying equal but opposite currents and being separated by a distance 3 times the loop radius.
There have been at least the following two problems with a Maxwell pair. One of them is that the gradient coils of a Maxwell pair is usually constructed with an additional coil wound at a larger radius and carrying a current so as to cancel the magnetic field exterior to the coil structure and the presence of such shield windings affects the condition for linearity of the gradient of the magnetic field being generated. The other of the problems is that a Maxwell pair thus shielded can be constructed as long as the diameter of the wire used for the pair is small enough compared to the radius of the coil, but this makes the gradient strength per ampere of current too small for NMR applications. If additional windings are to be added in order to enhance the field gradient, however, the spatial extent of these windings must also be small compared to the loop diameter of the pair.
It is therefore an object of this invention to provide a pair of extended coils, such that currents may reside along a length comparable to the loop diameter, capable of providing a magnetic field with a stronger uniform field gradient.
An extended Maxwell pair embodying this invention, with which the above and other objects can be accomplished, may be characterized as comprising a pair of cylindrical gradient coils disposed coaxially and adapted to carry equal currents in mutually opposite directions. Each of these gradient coils may be surrounded by a coaxially disposed cylindrically extended shield coil for canceling magnetic fields outside. For given values of radii of the gradient and shield coils, the length and the center-to-center separation of the pair of gradient coils are determined by numerically solving an equation which is derived from the condition that the currents through the gradient and shield coils should together generate a magnetic field inside with a linear gradient. The equation to be solved is derived by calculating the magnetic field by a Fourier-Bessel expansion method incorporating the condition that the shield coils do shield the magnetic field inside. The manner in which a wire should be wound to form the shield coils is determined from the numerical solution of the equation.